Questions on provisional Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories

Abstract

This is a supplement to [arXiv:1503.03676], where an approach towards a mathematically rigorous definition of the Coulomb branch of a $3$-dimensional $\mathcal{N}=4$ SUSY gauge theory was proposed. We ask questions on their expected properties, especially in relation to the corresponding Higgs branch, partly motivated by the interpretation of the level rank duality in terms of quiver varieties [arXiv:0809.2605] and the symplectic duality [arXiv:1407.0964]. We study questions in a few examples.

arXiv comment20 pages; ver.2 a minor correction

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Cited by in corpus (7)

• Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)
• Algebraic properties of the monopole formula
• Masses, Sheets and Rigid SCFTs
• Cherkis bow varieties and Coulomb branches of quiver gauge theories of affine type $A$
• Double affine Grassmannians and Coulomb branches of 3d N=4 quiver gauge theories
• Some Open Questions in Quiver Gauge Theory
• Note on some properties of generalized affine Grassmannian slices